Volume 7, Issue 1, February 2000, Pages 1 - 13
Lax Pairs, Painlevé Properties and Exact Solutions of the Calogero Korteweg-de Vries Equation and a New (2 + 1)-Dimensional Equation
- Song-Ju YU, Kouichi TODA
- Corresponding Author
- Song-Ju YU
Available Online 13 December 2006.
- https://doi.org/10.2991/jnmp.2000.7.1.1How to use a DOI?
- We prove the existence of a Lax pair for the Calogero Korteweg-de Vries (CKdV) equation. Moreover, we modify the T operator in the the Lax pair of the CKdV equation, in the search of a (2 + 1)-dimensional case and thereby propose a new equation in (2+1) dimensions. We named this the (2+1)-dimensional CKdV equation. We show that the CKdV equation as well as the (2+1)-dimensional CKdV equation are integrable in the sense that they possess the Painlevé property. Some exact solutions are also constructed.
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - Song-Ju YU AU - Kouichi TODA PY - 2006 DA - 2006/12 TI - Lax Pairs, Painlevé Properties and Exact Solutions of the Calogero Korteweg-de Vries Equation and a New (2 + 1)-Dimensional Equation JO - Journal of Nonlinear Mathematical Physics SP - 1 EP - 13 VL - 7 IS - 1 SN - 1402-9251 UR - https://doi.org/10.2991/jnmp.2000.7.1.1 DO - https://doi.org/10.2991/jnmp.2000.7.1.1 ID - YU2006 ER -